SOLUTION: Hello, I would appreciate it very much if someone could help me with this problem. Is a measure of 26 inches​ "far away" from a mean of 16 ​inches? As someone with knowle

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Question 1141014: Hello,
I would appreciate it very much if someone could help me with this problem.
Is a measure of 26 inches​ "far away" from a mean of 16 ​inches? As someone with knowledge of​ statistics, you answer​ "it depends" and request the standard deviation of the underlying data.
​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 ​inches?
​(b) Is 26 inches far away from a mean of 16 ​inches?
​(c) Suppose the standard deviation of the underlying data is 8 inches. Is 26 inches far away from a mean of 16 ​inches?
Thank you SO much!
​
Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
​(a) Suppose the data come from a sample whose standard deviation is 2 inches. How many standard deviations is 26 inches from 16 ​inches?

It is five standard deviations away. This is because 26 inches is 10 inches away from 16 inches, and 10 divided by 2 (which is one standard deviation) is 5.

​(b) Is 26 inches far away from a mean of 16 ​inches?

With a standard deviation of 2, it is VERY far away. (See above...FIVE standard deviations away.) Less than 0.1% of all values would be expected to exceed 26 inches.

(c) Suppose the standard deviation of the underlying data is 8 inches. Is 26 inches far away from a mean of 16 ​inches?

With a standard deviation of 8 inches, a value of 26 inches is 1.25 standard deviations away. (26 inches is 10 inches away from 16 inches, and 10 divided by 8 is 1.25.)

With a standard deviation of 8, about 10% of values would be expected to exceed 26 inches. Furthermore, with a standard deviation of 8, about 80% of the values would be expected to fall between 6 and 26 inches.
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